# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for the Earth and Planetary Sciences
# Copyright (C) 2012 - 2017 by the BurnMan team, released under the GNU
# GPL v2 or later.
from __future__ import absolute_import
import numpy as np
from .mineral import Mineral, material_property
from .solutionmodel import SolutionModel
from .solutionmodel import MechanicalSolution, IdealSolution
from .solutionmodel import SymmetricRegularSolution, AsymmetricRegularSolution
from .solutionmodel import SubregularSolution
from .processchemistry import sum_formulae
from .averaging_schemes import reuss_average_function
[docs]class SolidSolution(Mineral):
"""
This is the base class for all solid solutions.
Site occupancies, endmember activities and the constant
and pressure and temperature dependencies of the excess
properties can be queried after using set_composition()
States of the solid solution can only be queried after setting
the pressure, temperature and composition using set_state().
This class is available as :class:`burnman.SolidSolution`.
It uses an instance of :class:`burnman.SolutionModel` to
calculate interaction terms between endmembers.
All the solid solution parameters are expected to be in SI units. This
means that the interaction parameters should be in J/mol, with the T
and P derivatives in J/K/mol and m^3/mol.
"""
def __init__(self,
name=None,
solution_type=None,
endmembers=None,
energy_interaction=None,
volume_interaction=None,
entropy_interaction=None,
alphas=None,
molar_fractions=None):
"""
Set up matrices to speed up calculations for when P, T, X is defined.
Parameters
----------
endmembers: list of :class:`burnman.Mineral`
List of endmembers in this solid solution.
solution_model: :class:`burnman.SolutionModel`
SolutionModel to use.
"""
Mineral.__init__(self)
# SolidSolution needs a method attribute to call Mineral.set_state().
# Note that set_method() below will not change self.method
self.method = 'SolidSolutionMethod'
if name is not None:
self.name = name
if solution_type is not None:
self.solution_type = solution_type
if endmembers is not None:
self.endmembers = endmembers
if energy_interaction is not None:
self.energy_interaction = energy_interaction
if volume_interaction is not None:
self.volume_interaction = volume_interaction
if entropy_interaction is not None:
self.entropy_interaction = entropy_interaction
if alphas is not None:
self.alphas = alphas
if endmembers is not None:
self.endmembers = endmembers
if hasattr(self, 'endmembers') is False:
raise Exception(
"'endmembers' attribute missing from solid solution")
try:
self.endmember_formulae = [
mbr[0].params['formula'] for mbr in self.endmembers]
except KeyError:
raise Exception(
"Not all endmembers of this solid solution have a formula in their params dictionary.")
# Set default solution model type
if hasattr(self, 'solution_type'):
if self.solution_type == 'mechanical':
self.solution_model = MechanicalSolution(self.endmembers)
elif self.solution_type == 'ideal':
self.solution_model = IdealSolution(self.endmembers)
else:
if hasattr(self, 'energy_interaction') is False:
self.energy_interaction = None
if hasattr(self, 'volume_interaction') is False:
self.volume_interaction = None
if hasattr(self, 'entropy_interaction') is False:
self.entropy_interaction = None
if self.solution_type == 'symmetric':
self.solution_model = SymmetricRegularSolution(
self.endmembers, self.energy_interaction, self.volume_interaction, self.entropy_interaction)
elif self.solution_type == 'asymmetric':
if hasattr(self, 'alphas') is False:
raise Exception(
"'alphas' attribute missing from solid solution")
self.solution_model = AsymmetricRegularSolution(
self.endmembers, self.alphas, self.energy_interaction, self.volume_interaction, self.entropy_interaction)
elif self.solution_type == 'subregular':
self.solution_model = SubregularSolution(
self.endmembers, self.energy_interaction, self.volume_interaction, self.entropy_interaction)
else:
raise Exception(
"Solution model type " + self.solution_type + "not recognised.")
else:
self.solution_model = SolutionModel()
# Number of endmembers in the solid solution
self.n_endmembers = len(self.endmembers)
try:
self.endmember_names = [mbr[0].name for mbr in self.endmembers]
except AttributeError:
pass
# Equation of state
for i in range(self.n_endmembers):
self.endmembers[i][0].set_method(
self.endmembers[i][0].params['equation_of_state'])
# Molar fractions
if molar_fractions is not None:
self.set_composition(molar_fractions)
[docs] def get_endmembers(self):
return self.endmembers
[docs] def set_composition(self, molar_fractions):
"""
Set the composition for this solid solution.
Resets cached properties
Parameters
----------
molar_fractions: list of float
molar abundance for each endmember, needs to sum to one.
"""
assert(len(self.endmembers) == len(molar_fractions))
if self.solution_type != 'mechanical':
assert(sum(molar_fractions) > 0.9999)
assert(sum(molar_fractions) < 1.0001)
self.reset()
self.molar_fractions = np.array(molar_fractions)
[docs] def set_method(self, method):
for i in range(self.n_endmembers):
self.endmembers[i][0].set_method(method)
# note: do not set self.method here!
self.reset()
[docs] def set_state(self, pressure, temperature):
Mineral.set_state(self, pressure, temperature)
for i in range(self.n_endmembers):
self.endmembers[i][0].set_state(pressure, temperature)
@material_property
def formula(self):
"""
Returns molar chemical formula of the solid solution
"""
return sum_formulae(self.endmember_formulae, self.molar_fractions)
@material_property
def activities(self):
"""
Returns a list of endmember activities [unitless]
"""
return self.solution_model.activities(self.pressure, self.temperature, self.molar_fractions)
@material_property
def activity_coefficients(self):
"""
Returns a list of endmember activity coefficients (gamma = activity / ideal activity) [unitless]
"""
return self.solution_model.activity_coefficients(self.pressure, self.temperature, self.molar_fractions)
@material_property
def molar_internal_energy(self):
"""
Returns molar internal energy of the mineral [J/mol]
Aliased with self.energy
"""
return self.molar_helmholtz + self.temperature * self.molar_entropy
@material_property
def excess_partial_gibbs(self):
"""
Returns excess partial molar gibbs free energy [J/mol]
Property specific to solid solutions.
"""
return self.solution_model.excess_partial_gibbs_free_energies(self.pressure, self.temperature, self.molar_fractions)
@material_property
def excess_partial_volumes(self):
"""
Returns excess partial volumes [m^3]
Property specific to solid solutions.
"""
return self.solution_model.excess_partial_volumes(self.pressure, self.temperature, self.molar_fractions)
@material_property
def excess_partial_entropies(self):
"""
Returns excess partial entropies [J/K]
Property specific to solid solutions.
"""
return self.solution_model.excess_partial_entropies(self.pressure, self.temperature, self.molar_fractions)
@material_property
def partial_gibbs(self):
"""
Returns excess partial molar gibbs free energy [J/mol]
Property specific to solid solutions.
"""
return np.array([self.endmembers[i][0].gibbs for i in range(self.n_endmembers)]) + self.excess_partial_gibbs
@material_property
def partial_volumes(self):
"""
Returns excess partial volumes [m^3]
Property specific to solid solutions.
"""
return np.array([self.endmembers[i][0].molar_volume for i in range(self.n_endmembers)]) + self.excess_partial_volumes
@material_property
def partial_entropies(self):
"""
Returns excess partial entropies [J/K]
Property specific to solid solutions.
"""
return np.array([self.endmembers[i][0].molar_entropy for i in range(self.n_endmembers)]) + self.excess_partial_entropies
@material_property
def excess_gibbs(self):
"""
Returns molar excess gibbs free energy [J/mol]
Property specific to solid solutions.
"""
return self.solution_model.excess_gibbs_free_energy(self.pressure, self.temperature, self.molar_fractions)
@material_property
def gibbs_hessian(self):
"""
Returns an array containing the second compositional derivative
of the Gibbs free energy [J]. Property specific to solid solutions.
"""
return self.solution_model.gibbs_hessian(self.pressure, self.temperature, self.molar_fractions)
@material_property
def entropy_hessian(self):
"""
Returns an array containing the second compositional derivative
of the entropy [J/K]. Property specific to solid solutions.
"""
return self.solution_model.entropy_hessian(self.pressure, self.temperature, self.molar_fractions)
@material_property
def volume_hessian(self):
"""
Returns an array containing the second compositional derivative
of the volume [m^3]. Property specific to solid solutions.
"""
return self.solution_model.volume_hessian(self.pressure, self.temperature, self.molar_fractions)
@material_property
def molar_gibbs(self):
"""
Returns molar Gibbs free energy of the solid solution [J/mol]
Aliased with self.gibbs
"""
return sum([self.endmembers[i][0].gibbs * self.molar_fractions[i] for i in range(self.n_endmembers)]) + self.excess_gibbs
@material_property
def molar_helmholtz(self):
"""
Returns molar Helmholtz free energy of the solid solution [J/mol]
Aliased with self.helmholtz
"""
return self.molar_gibbs - self.pressure * self.molar_volume
@material_property
def molar_mass(self):
"""
Returns molar mass of the solid solution [kg/mol]
"""
return sum([self.endmembers[i][0].molar_mass * self.molar_fractions[i] for i in range(self.n_endmembers)])
@material_property
def excess_volume(self):
"""
Returns excess molar volume of the solid solution [m^3/mol]
Specific property for solid solutions
"""
return self.solution_model.excess_volume(self.pressure, self.temperature, self.molar_fractions)
@material_property
def molar_volume(self):
"""
Returns molar volume of the solid solution [m^3/mol]
Aliased with self.V
"""
return sum([self.endmembers[i][0].molar_volume * self.molar_fractions[i] for i in range(self.n_endmembers)]) + self.excess_volume
@material_property
def density(self):
"""
Returns density of the solid solution [kg/m^3]
Aliased with self.rho
"""
return self.molar_mass / self.molar_volume
@material_property
def excess_entropy(self):
"""
Returns excess molar entropy [J/K/mol]
Property specific to solid solutions.
"""
return self.solution_model.excess_entropy(self.pressure, self.temperature, self.molar_fractions)
@material_property
def molar_entropy(self):
"""
Returns molar entropy of the solid solution [J/K/mol]
Aliased with self.S
"""
return sum([self.endmembers[i][0].S * self.molar_fractions[i] for i in range(self.n_endmembers)]) + self.excess_entropy
@material_property
def excess_enthalpy(self):
"""
Returns excess molar enthalpy [J/mol]
Property specific to solid solutions.
"""
return self.solution_model.excess_enthalpy(self.pressure, self.temperature, self.molar_fractions)
@material_property
def molar_enthalpy(self):
"""
Returns molar enthalpy of the solid solution [J/mol]
Aliased with self.H
"""
return sum([self.endmembers[i][0].H * self.molar_fractions[i] for i in range(self.n_endmembers)]) + self.excess_enthalpy
@material_property
def isothermal_bulk_modulus(self):
"""
Returns isothermal bulk modulus of the solid solution [Pa]
Aliased with self.K_T
"""
return self.V * 1. / (sum([self.endmembers[i][0].V / (self.endmembers[i][0].K_T) * self.molar_fractions[i] for i in range(self.n_endmembers)]))
@material_property
def adiabatic_bulk_modulus(self):
"""
Returns adiabatic bulk modulus of the solid solution [Pa]
Aliased with self.K_S
"""
if self.temperature < 1e-10:
return self.isothermal_bulk_modulus
else:
return self.isothermal_bulk_modulus * self.molar_heat_capacity_p / self.molar_heat_capacity_v
@material_property
def isothermal_compressibility(self):
"""
Returns isothermal compressibility of the solid solution (or inverse isothermal bulk modulus) [1/Pa]
Aliased with self.K_T
"""
return 1. / self.isothermal_bulk_modulus
@material_property
def adiabatic_compressibility(self):
"""
Returns adiabatic compressibility of the solid solution (or inverse adiabatic bulk modulus) [1/Pa]
Aliased with self.K_S
"""
return 1. / self.adiabatic_bulk_modulus
@material_property
def shear_modulus(self):
"""
Returns shear modulus of the solid solution [Pa]
Aliased with self.G
"""
G_list = np.fromiter(
(e[0].G for e in self.endmembers), dtype=float, count=self.n_endmembers)
return reuss_average_function(self.molar_fractions, G_list)
@material_property
def p_wave_velocity(self):
"""
Returns P wave speed of the solid solution [m/s]
Aliased with self.v_p
"""
return np.sqrt((self.adiabatic_bulk_modulus
+ 4. / 3. * self.shear_modulus) / self.density)
@material_property
def bulk_sound_velocity(self):
"""
Returns bulk sound speed of the solid solution [m/s]
Aliased with self.v_phi
"""
return np.sqrt(self.adiabatic_bulk_modulus / self.density)
@material_property
def shear_wave_velocity(self):
"""
Returns shear wave speed of the solid solution [m/s]
Aliased with self.v_s
"""
return np.sqrt(self.shear_modulus / self.density)
@material_property
def grueneisen_parameter(self):
"""
Returns grueneisen parameter of the solid solution [unitless]
Aliased with self.gr
"""
if self.temperature < 1e-10:
return float('nan')
else:
return self.thermal_expansivity * self.isothermal_bulk_modulus * self.molar_volume / self.molar_heat_capacity_v
@material_property
def thermal_expansivity(self):
"""
Returns thermal expansion coefficient (alpha) of the solid solution [1/K]
Aliased with self.alpha
"""
return (1. / self.V) * sum([self.endmembers[i][0].alpha * self.endmembers[i][0].V * self.molar_fractions[i] for i in range(self.n_endmembers)])
@material_property
def molar_heat_capacity_v(self):
"""
Returns molar heat capacity at constant volume of the solid solution [J/K/mol]
Aliased with self.C_v
"""
return self.molar_heat_capacity_p - self.molar_volume * self.temperature * self.thermal_expansivity * self.thermal_expansivity * self.isothermal_bulk_modulus
@material_property
def molar_heat_capacity_p(self):
"""
Returns molar heat capacity at constant pressure of the solid solution [J/K/mol]
Aliased with self.C_p
"""
return sum([self.endmembers[i][0].molar_heat_capacity_p * self.molar_fractions[i] for i in range(self.n_endmembers)])